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MARL-CC: A Mathematical Framework forMulti-Agent Reinforcement Learning in ConnectedAutonomous Vehicles: Addressing Nonlinearity,Partial Observability, and Credit Assignment forOptimal Control

Mazyar Taghavi, Javad Vahidi

TL;DR

MARL-CC presents a rigorous, control-informed multi-agent reinforcement learning framework for connected autonomous vehicles that tackles nonlinear dynamics, partial observability, and inter-agent coupling. By integrating differential geometric control, probabilistic belief inference, and Shapley-value-based credit assignment within a centralized training–decentralized execution paradigm, MARL-CC delivers convergence guarantees, Lyapunov-based stability, and robust performance under delays and uncertainty. The approach yields up to 40% faster convergence and improved cooperative efficiency over baselines like PPO, DDPG, and QMIX, with extensive simulations and sim-to-real validation demonstrating practical viability. This work offers a scalable, interpretable, and safe pathway toward distributed autonomous mobility in ITS, UAV coordination, and distributed robotics, with open-source code to support reproducibility.

Abstract

Multi-Agent Reinforcement Learning (MARL) has emerged as a powerfulparadigm for cooperative decision-making in connected autonomous vehicles(CAVs); however, existing approaches often fail to guarantee stability, optimality,and interpretability in systems characterized by nonlinear dynamics,partial observability, and complex inter-agent coupling. This study addressesthese foundational challenges by introducing MARL-CC, a unified MathematicalFramework for Multi-Agent Reinforcement Learning with Control Coordination.The proposed framework integrates differential geometric control, Bayesian inference,and Shapley-value-based credit assignment within a coherent optimizationarchitecture, ensuring bounded policy updates, decentralized belief estimation,and equitable reward distribution. Theoretical analyses establish convergence andstability guarantees under stochastic disturbances and communication delays.Empirical evaluations across simulation and real-world testbeds demonstrate upto a 40% improvement in convergence rate and enhanced cooperative efficiencyover leading baselines, including PPO, DDPG, and QMIX.These results signify a decisive advance in control-oriented reinforcement learning,bridging the gap between mathematical rigor and practical autonomy.The MARL-CC framework provides a scalable foundation for intelligent transportation,UAV coordination, and distributed robotics, paving the way toward interpretable, safe, and adaptive multi-agent systems. All codes and experimentalconfigurations are publicly available on GitHub to support reproducibilityand future research.

MARL-CC: A Mathematical Framework forMulti-Agent Reinforcement Learning in ConnectedAutonomous Vehicles: Addressing Nonlinearity,Partial Observability, and Credit Assignment forOptimal Control

TL;DR

MARL-CC presents a rigorous, control-informed multi-agent reinforcement learning framework for connected autonomous vehicles that tackles nonlinear dynamics, partial observability, and inter-agent coupling. By integrating differential geometric control, probabilistic belief inference, and Shapley-value-based credit assignment within a centralized training–decentralized execution paradigm, MARL-CC delivers convergence guarantees, Lyapunov-based stability, and robust performance under delays and uncertainty. The approach yields up to 40% faster convergence and improved cooperative efficiency over baselines like PPO, DDPG, and QMIX, with extensive simulations and sim-to-real validation demonstrating practical viability. This work offers a scalable, interpretable, and safe pathway toward distributed autonomous mobility in ITS, UAV coordination, and distributed robotics, with open-source code to support reproducibility.

Abstract

Multi-Agent Reinforcement Learning (MARL) has emerged as a powerfulparadigm for cooperative decision-making in connected autonomous vehicles(CAVs); however, existing approaches often fail to guarantee stability, optimality,and interpretability in systems characterized by nonlinear dynamics,partial observability, and complex inter-agent coupling. This study addressesthese foundational challenges by introducing MARL-CC, a unified MathematicalFramework for Multi-Agent Reinforcement Learning with Control Coordination.The proposed framework integrates differential geometric control, Bayesian inference,and Shapley-value-based credit assignment within a coherent optimizationarchitecture, ensuring bounded policy updates, decentralized belief estimation,and equitable reward distribution. Theoretical analyses establish convergence andstability guarantees under stochastic disturbances and communication delays.Empirical evaluations across simulation and real-world testbeds demonstrate upto a 40% improvement in convergence rate and enhanced cooperative efficiencyover leading baselines, including PPO, DDPG, and QMIX.These results signify a decisive advance in control-oriented reinforcement learning,bridging the gap between mathematical rigor and practical autonomy.The MARL-CC framework provides a scalable foundation for intelligent transportation,UAV coordination, and distributed robotics, paving the way toward interpretable, safe, and adaptive multi-agent systems. All codes and experimentalconfigurations are publicly available on GitHub to support reproducibilityand future research.

Paper Structure

This paper contains 90 sections, 12 theorems, 73 equations, 4 figures, 7 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Background and Motivation
  3. Key Challenges
  4. Research Gap
  5. Contributions of the Paper
  6. Related Works
  7. Reinforcement Learning for Vehicle Control
  8. Multi-Agent Reinforcement Learning (MARL) in Connected Systems
  9. Mathematical and Control-Theoretic Approaches
  10. Identified Research Gap
  11. Mathematical Foundations
  12. System Model of Connected Autonomous Vehicles
  13. Nonlinear Optimal Control Objective
  14. Partial Observability and Communication Constraints
  15. Cooperative Reward Structure
  16. ...and 75 more sections

Key Result

Proposition 1

Under smoothness and boundedness assumptions on $f_i$ and $\ell_i$, there exists a measurable control $u_i^*(t)$ that minimizes $J_i$ for all $i \in \mathcal{N}$isidori1995nonlinear.

Figures (4)

  • Figure 1: Architecture of MARL-CC for connected autonomous vehicles. Each agent integrates local observations, belief updates, nonlinear optimal control, and Shapley-value-based reward allocation to achieve cooperative optimal control.
  • Figure 2: Convergence comparison of MARL-CC and baseline algorithms over $10^5$ training episodes. MARL-CC exhibits accelerated convergence and smoother reward evolution due to stability-aware optimization and differential geometric control.
  • Figure 3: Convergence trajectories of MARL-CC and baseline configurations. The full MARL-CC framework exhibits smooth monotonic convergence with low variance, reaching 95% performance at 4.8k episodes. Ablated variants and baselines demonstrate oscillations and slower convergence, highlighting the importance of each component.
  • Figure 4: Performance metrics comparison across MARL algorithms, showing normalized reward convergence and stability trends over training episodes. The MARL-CC algorithm demonstrates superior performance and faster convergence relative to classical baselines.

Theorems & Definitions (21)

  • Definition 1: Neighbor Coupling
  • Example 1
  • Proposition 1: Existence of Optimal Control
  • Theorem 2: Shapley Value Fairness
  • Corollary 1: Boundedness of Trajectories
  • Definition 2: Lie Derivative
  • Theorem 3: Stabilizing Feedback Equivalence
  • proof
  • Theorem 4: Local Asymptotic Stability
  • proof
  • ...and 11 more